# A Two-Level Hierarchical Linear Model Analysis of the Effect of Teacher Factors, Student Factors, and Facility Conditions on Students’ Cognitive Scores in Rural China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review and Research Hypothesis

#### 2.1. The Influence of Student and Teaches Factors on Students’ Cognitive Performance

**Hypothesis**

**1**

**(H1).**

**Hypothesis**

**2**

**(H2).**

**Hypothesis**

**3**

**(H3).**

**Hypothesis**

**4**

**(H4).**

**Hypothesis**

**5**

**(H5).**

**Hypothesis**

**6**

**(H6).**

**Hypothesis**

**7**

**(H7).**

#### 2.2. The Contribution of Facility Conditions to Students’ Cognitive Performance

**Hypothesis**

**8**

**(H8).**

**Hypothesis**

**9**

**(H9).**

**Hypothesis**

**10**

**(H10).**

## 3. Research Methodology

#### 3.1. Data Source and Sample Distribution

#### 3.2. Research Variables and Analytical Framework

#### Research Variables

#### 3.3. Econometric Model

#### 3.3.1. HLM

_{ij}represents the cognitive scores of the ith student in J school. SE is the student’s gender, PEO is the student’s nationality, DS represents only child status, AT is the student’s learning attitude, LO indicates participation in logic classes, LA indicates participation in language classes, AR indicates participation in art classes, BOOS represents the number of books at the student’s home, TEST is the teacher–student ratio, JZ represents whether the teacher teaches more than one class concurrently, BEN is teacher’s educational experience, GJZC is teacher’s title, WTE is teacher’s gender, SF is teacher’s major, AGE is teacher’s teaching age, SYB is teacher’s status, SJB is books per student, JXSB represents teaching equipment, JSGM represents class size, and JXYJ represents school real estate.

#### 3.3.2. Shapley Method

## 4. Results

#### 4.1. Analysis of Factors That Affect Student Scores without Model Parameter Estimates

^{2}= 8421.21221, p < 0.01). The estimated within-group variance is 0.51135, the between-column variance is 0.23821, and the intraclass correlation coefficient is 0.3178, the latter indicating that 32% of the total variation in the students’ cognitive scores comes from differences between classes. That class characteristics have a statistically significant impact on students’ cognitive test scores, which makes these data suitable for analysis with multilevel models.

#### 4.2. The Influence of Student and Teacher Factors on Students’ Scores

#### 4.3. The Influence of Facility Conditions

#### 4.4. The Contributions of Student, Teacher Facors, and Facility Conditions to Students’ Cognitive Scores

## 5. Limitations, Conclusions, and Recommendations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Zhang, Y.M.; Hao, Y.; Li, M.J. A Empirical Study on the Impact of Teacher’s and Student’s Factors to Their Academic Performance—Based on A Multi-Linear Analysis to A Large Scale Test Data. Teach. Educ. Res.
**2014**, 24, 56–62. [Google Scholar] - Kwon, M.; Kim, H. Indicators as cultural capital that affect academic achievement: Focusing on multicultural families. Korean Educ. Inq.
**2014**, 32, 29–53. [Google Scholar] - Wang, A.; Wang, X. The Imbalance between Personnel and Substance Allocation in the Supply of Rural Education and the Way of Balance. Mod. Educ. Manag.
**2019**, 7, 9–13. [Google Scholar] - Dorff, E.N.; Mackler, A.L. Responsibilities for the provision of health care. Shma
**2003**, 33, 7–8. Available online: https://pubmed.ncbi.nlm.nih.gov/14603941/ (accessed on 27 May 2022). - Haahr, J.H.; Nielsen, T.K.; Jakobsen, S.T.; Hansen, M.E. Explaining Student Performance: Evidence from the International PISA, TIMSS and PIRLS Surveys. Danish Technological Institute. 2005. Available online: https://www.oecd.org/education/school/programmeforinternationalstudentassessmentpisa/35920726.pdf (accessed on 27 May 2022).
- OECD. PISA School Factors Related to Quality and Equity: Results from PISA 2000; OECD: Paris, France, 2005. [Google Scholar]
- Deng, Y.T. Empirical Research on the Relationship between Teacher and School Quality. Master’s Thesis, Peking University, Beijing, China, 2005. [Google Scholar]
- Chu, J.H.; Loyalka, P.; Chu, J.Y.; Qu, Q.; Shi, Y.; Li, G. The impact of teacher credentials on student achievement in China. China Econ. Rev.
**2015**, 36, 14–24. [Google Scholar] [CrossRef] - Hanushek, E.; Rivkin, S. Using Value-Added Measures of Teacher Quality (CALDER Brief# 9); Urban Institute: Washington, DC, USA, 2010; Available online: https://www.urban.org/sites/default/files/publication/33216/1001371-Using-Value-Added-Measures-of-Teacher-Quality.PDF (accessed on 27 May 2022).
- Rivkin, S.G.; Hanushek, E.A.; Kain, J.F. Teachers, schools, and academic achievement. Econometerica
**2005**, 73, 417–458. [Google Scholar] [CrossRef] - Luschei, T.F. The effectiveness and distribution of male primary teachers: Evidence from two Mexican states. Int. J. Educ. Dev.
**2012**, 32, 145–154. [Google Scholar] [CrossRef] - Cushman, P. Let’s hear it from the males: Issues facing male primary school teachers. Teach. Teach. Educ.
**2005**, 21, 227–240. [Google Scholar] [CrossRef] - Karlidag-Dennis, E.; Hazenberg, R.; Dinh, A.-T. Is education for all? The experiences of ethnic minority students and teachers in North-western Vietnam engaging with social entrepreneurship. Int. J. Educ. Dev.
**2020**, 77, 102224. [Google Scholar] [CrossRef] - Bai, S.N.; Han, J.W.; Can-Hui, L.I. A Study of the Influence of Teachers’ Variables on Students’ Mathematics Achievement. Teach. Educ. Res.
**2019**, 31, 70–85. [Google Scholar] - Hardré, P.L.; Sullivan, D.W. Student differences and environment perceptions: How they contribute to student motivation in rural high schools. Learn. Individ. Differ.
**2008**, 18, 471–485. [Google Scholar] [CrossRef] - Mullola, S.; Jokela, M.; Ravaja, N.; Lipsanen, J.; Hintsanen, M.; Alatupa, S.; Keltikangas-Järvinen, L. Associations of student temperament and educational competence with academic achievement: The role of teacher age and teacher and student gender. Teach. Teach. Educ.
**2011**, 27, 942–951. [Google Scholar] [CrossRef] - Gevrek, Z.E.; Gevrek, D.; Neumeier, C. Explaining the gender gaps in mathematics achievement and attitudes: The role of societal gender equality. Econ. Educ. Rev.
**2020**, 76, 101978. [Google Scholar] [CrossRef] - Khudadad, N.; Mickelson, R.A. School built environment, gender, and student achievement in Pakistan. Int. J. Educ. Dev.
**2021**, 87, 102503. [Google Scholar] [CrossRef] - Birenbaum, M.; Nasser, F. Ethnic and gender differences in mathematics achievement and in dispositions towards the study of mathematics. Learn. Instr.
**2006**, 16, 26–40. [Google Scholar] [CrossRef] - Workman, J. Social costs to trying hard in high school: Differences by race-ethnicity. Soc. Sci. Res.
**2020**, 92, 102484. [Google Scholar] [CrossRef] - Egalite, A.J.; Kisida, B.; Winters, M.A. Representation in the classroom: The effect of own-race teachers on student achievement. Econ. Educ. Rev.
**2015**, 45, 44–52. [Google Scholar] [CrossRef] [Green Version] - Shi, J.; Li, L.; Wu, D.; Li, H. Are Only Children Always Better? Testing the Sibling Effects on Academic Performance in Rural Chinese Adolescents. Child. Youth Serv. Rev.
**2021**, 131, 106291. [Google Scholar] [CrossRef] - Xu, J.Z. A profile analysis of online assignment motivation: Combining achievement goal and expectancy-value perspectives. Comput. Educ.
**2022**, 177, 104367. [Google Scholar] [CrossRef] - Lipnevich, A.A.; Preckel, F.; Krumm, S. Mathematics attitudes and their unique contribution to achievement: Going over and above cognitive ability and personality. Learn. Individ. Differ.
**2016**, 47, 70–79. [Google Scholar] [CrossRef] - Poon, K. The impact of socioeconomic status on parental factors in promoting academic achievement in Chinese children. Int. J. Educ. Dev.
**2020**, 75, 102175. [Google Scholar] [CrossRef] - Fang, S.; Huang, J.; Wu, S.; Jin, M.; Kim, Y.; Henrichsen, C. Family assets, parental expectation, and child educational achievement in China: A validation of mediation analyses. Child. Youth Serv. Rev.
**2020**, 112, 104875. [Google Scholar] [CrossRef] - Raposo, I.P.D.A.; Gonçalves, M.B.C. Peer effects and educational achievement: Evidence of causal effects using age at school entry as exogenous variation for Peer quality. EconomiA
**2020**, 21, 18–37. [Google Scholar] [CrossRef] - Darling-Hammond, L. Teacher quality and student achievement. Educ. Policy Anal. Arch.
**2000**, 8. Available online: https://epaa.asu.edu/index.php/epaa/article/view/392 (accessed on 27 May 2022). [CrossRef] [Green Version] - Liang, W.Y. Value-added evaluation of teachers’ influence on students’ academic performance: Panel data from rural primary schools in five western provinces of China. In Proceedings of the 2009 China Educational Economics Annual Conference, Guangzhou, China, 5 December 2009; pp. 58–597. [Google Scholar]
- Gong, X.; Ding, Y.; Tsang, M.C. Gender differences of academic performance in compulsory education in rural Southwestern China. Int. J. Educ. Dev.
**2014**, 39, 193–204. [Google Scholar] [CrossRef] - Zhang, W.J.; Xin, T.; Kang, C.H. The impact of teacher variables on the fourth-grade math achievement: A value-added study. J. Educ. Stud.
**2010**, 6, 69–76. [Google Scholar] - Xue, H.P.; Wang, D.; Wu, X.W. The Impact of private tutoring on left-behind students’ academic achievement in Chinese compilsory education. Peking Univ. Educ. Rev.
**2014**, 12, 189–190. [Google Scholar] - Pang, W.G.; Xu, X.B.; Lin, L.J.; Ren, Y.Q. The impact of family socioeconomic status on students’ academic achievement. Glob. Educ.
**2013**, 42, 12–21. [Google Scholar] - Pang, X.P.; Yan, R.H.; Nie, J.C.; Luo, S.G.; Zhang, L.X.; Shi, Y.J.; Pang, X.D. Can private tutoring improve students’ academic achievement in rural primary school? China Econ. Educ. Rev.
**2017**, 2, 87–101. [Google Scholar] - Li, J.; Shi, Z.; Xue, E. The problems, needs and strategies of rural teacher development at deep poverty areas in China: Rural schooling stakeholder perspectives. Int. J. Educ. Res.
**2019**, 99, 101496. [Google Scholar] [CrossRef] - Lin, X.; Xie, J.; Lin, S. The influence of family capital on rural children’s academic achievements-an empirical research based on the data of CFPS. Theory Pract. Educ.
**2018**, 41, 24–30. [Google Scholar] - Yang, Z.C. The Intermediary factors of family background affects the students’ development. China Econ. Educ. Rev.
**2018**, 3, 61–82. [Google Scholar] - Xie, B.C. Research on the Influence of Family Capital, Shadow Education towards Children’s Learning Grades. Master’s Thesis, Xiangtan University, Xiangtan, China, 2019. [Google Scholar]
- Li, Y.; Yang, Y.L.; Wu, S.R. Problems and countermeasures of the allocation efficiency of high-quality resources in urban and rural compulsory education: Based on DEA-malmquist model. J. Chin. Soc. Educ.
**2021**, 1, 60–65. [Google Scholar] - Grubb, W.N. Multiple resources, multiple outcomes: Testing the “improved” school finance with NELS88. Am. Educ. Res. J.
**2008**, 45, 104–144. [Google Scholar] [CrossRef] - De Witte, K.; Kortelainen, M. What explains the performance of students in a heterogeneous environment? Conditional efficiency estimation with continuous and discrete environmental variables. Appl. Econ.
**2013**, 45, 2401–2412. [Google Scholar] [CrossRef] - Hanushek, E.A. Interpreting recent research on schooling in developing countries. World Bank Res. Obs.
**1995**, 10, 227–246. [Google Scholar] [CrossRef] [Green Version] - Velez, E.; Schiefelbein, E.; Valenzuela, J. Factors Affecting Achievement in Primary Education (No. 12186); The World Bank: Washington, DC, USA, 1993; p. 1. [Google Scholar]
- Jiang, M.H. Education Cost Analysis; Higher Education Press: Beijing, China, 2020. [Google Scholar]
- Yang, S.H. The impacts of teacher’s human capital on student academic achievement: A study on education production function for junior middle schools in China’s western rural areas. In Proceedings of the 2010 China Educational Economics Annual Conference, Wuhan, China, 4 December 2010; pp. 1395–1408. [Google Scholar]
- Knoeppel, R.C.; Verstegen, D.A.; Rinehart, J.S. What is the relationship between resources and student achievement? A canonical analysis. J. Educ. Financ.
**2007**, 33, 183–202. [Google Scholar] - Hu, Y.M.; Du, Y.H. Empirical research on the educational production function of rural primary schools in Western China. Educ. Res.
**2009**, 30, 58–67. [Google Scholar] - Hu, Y.M. The relationship between school resources allocation and students’ attainment—Empirical research based on rural school survey of five provinces in West China. Ph.D. Thesis, Beijing Normal University, Beijing, China, 2007. [Google Scholar]
- Ma, H.M. The effect of teachers’ on-the-job training on students’ academic performance: Based on the evidence from the rural areas in Gansu Province. Teach. Dev. Res.
**2020**, 4, 94–105. [Google Scholar] - Fan, Y.L. A Relational Study on the Investment of Teacher Resources and the Output of Students’ Academic Achievement. Master’s Thesis, Henan University, Zhengzhou, China, 2007. [Google Scholar]
- Martorell, P.; Stange, K.; McFarlin Jr, I. Investing in schools: Capital spending, facility conditions, and student achievement. J. Public Econ.
**2016**, 140, 13–29. [Google Scholar] [CrossRef] [Green Version] - Neilson, C.A.; Zimmerman, S.D. The effect of school construction on test scores, school enrollment, and home prices. J. Public Econ.
**2014**, 120, 18–31. [Google Scholar] [CrossRef] [Green Version] - Fang, Z. The effect of class size on students’ non-cognitive skills. Moral Educ. China
**2016**, 8, 29–33. [Google Scholar] - Sanfo, J.-B.M. Connecting family, school, gold mining community and primary school students’ reading achievements in Burkina Faso–A three-level hierarchical linear model analysis. Int. J. Educ. Dev.
**2021**, 84, 102442. [Google Scholar] [CrossRef] - Sanfo, J.-B.M. A three-level hierarchical linear model analysis of the effect of school principals’ factors on primary school students’ learning achievements in Burkina Faso. Int. J. Educ. Res.
**2020**, 100, 101531. [Google Scholar] [CrossRef] - Barakat, B.; Cuaresma, J.C. Credit where credit is due: An approach to education returns based on Shapley values. Educ. Econ.
**2017**, 25, 1–9. [Google Scholar] [CrossRef] [Green Version] - Shieh, J.I.; Wu, H.H. Improving dual importance analysis based on a Shapley value associated with a fuzzy measure when interactions of criteria are significant. Int. J. Ind. Syst. Eng.
**2019**, 31, 168–183. [Google Scholar] - Giudici, P.; Raffinetti, E. Shapley-Lorenz eXplainable Artificial Intelligence. Expert Syst. Appl.
**2020**, 167, 114104. [Google Scholar] [CrossRef] - Mazalov, V.V.; Gusev, V.V. Generating functions and Owen value in cooperative network cover game. Perform. Eval.
**2020**, 144, 102–135. [Google Scholar] [CrossRef] - Zhang, Y.M.; Tian, Y.; Li, M.J. School background factors and individual student factors Research on the effect of grades——Multilayer linear model analysis based on large-scale test data A. Educ. Sci. Res.
**2012**, 4, 41–46. [Google Scholar] - Gelman, A.; Hill, J. Data Analysis Using Regression and Multilevel/Hierarchical Models; Cambridge University Press: Cambridge, UK, 2007. [Google Scholar]

Variable Name | Level | Sample Size | Mean Value | Standard Deviation | Minimum Value | Maximum Value |
---|---|---|---|---|---|---|

Student gender | 1 | 17,664 | 0.49 | 0.50 | 0.00 | 1.00 |

Student nationality | 1 | 17,664 | 0.09 | 0.28 | 0.00 | 1.00 |

Only child or not | 1 | 17,664 | 0.56 | 0.50 | 0.00 | 1.00 |

Self-education expectation | 1 | 17,664 | 1.61 | 0.55 | 0.00 | 2.00 |

Learning attitude | 1 | 17,664 | 3.31 | 0.67 | 1.00 | 4.00 |

Logic cram school | 1 | 17,664 | 0.34 | 0.47 | 0.00 | 1.00 |

Art cram school | 1 | 17,664 | 0.30 | 0.46 | 0.00 | 1.00 |

Language cram school | 1 | 17,664 | 0.15 | 0.36 | 0.00 | 1.00 |

Extracurricular reading amount | 1 | 17,664 | 3.17 | 1.21 | 1.00 | 5.00 |

Teacher gender | 2 | 419 | 3.15 | 0.85 | 0.00 | 4.00 |

Teachers’ educational background | 2 | 419 | 0.33 | 0.47 | 0.00 | 1.00 |

Teachers’ major | 2 | 419 | 3.77 | 0.47 | 2.00 | 4.00 |

Teaching experience | 2 | 419 | 2.42 | 1.01 | 0.00 | 4.00 |

Teacher identity | 2 | 419 | 4.37 | 0.88 | 4.00 | 8.00 |

Part-time teachers | 2 | 419 | 0.89 | 0.51 | 0.00 | 3.50 |

Professional title | 2 | 419 | 0.58 | 0.81 | 0.00 | 3.00 |

Books per student | 2 | 112 | 96.55 | 362.49 | 4.18 | 5102.04 |

Teaching equipment | 2 | 112 | 3.55 | 0.89 | 1.00 | 4.00 |

Class sizes | 2 | 112 | 49.68 | 8.95 | 25.00 | 70.00 |

Laboratory | 2 | 112 | 2.62 | 0.51 | 1.00 | 3.00 |

Computer classroom | 2 | 112 | 2.58 | 0.56 | 1.00 | 3.00 |

Music room | 2 | 112 | 2.40 | 0.64 | 1.00 | 3.00 |

Student activity room | 2 | 112 | 1.97 | 0.70 | 1.00 | 3.00 |

Psychology consultation room | 2 | 112 | 2.21 | 0.61 | 1.00 | 3.00 |

Faculty–student ratio | 2 | 112 | 28.06 | 103.14 | 1.11 | 814.00 |

Variable Name | Variable Description and Scoring Method |
---|---|

Result variables | |

Standardized test scores | Standardized scores on students’ cognitive ability test |

Student level | |

Gender | From the student questionnaire a01: 0 = male, 1 = female |

Nationality | From the student questionnaire a03: 0 = Han, 1 = minority |

Only-child or not | From the student questionnaire b01: 0 = an only child, 1 = non-only child |

Self-education expectation | From the student questionnaire c22: 1 = left school now, 2 = junior high school graduation, 3 = medium college graduation/technical school graduation, 4 = vocational high school graduation, 5 = common senior high school, 6 = college diploma, 7 = undergraduate graduation, 8 = postgraduate students, 9 = doctor degree, 10 = do not mind. In the econometric model, take “below undergraduate” in education expectation as the reference group, which is defined as 0, and “undergraduate and above” self-education expectation is defined as 1. |

Learning attitude | From the student questionnaire a1201, 1202, and 1203: take a 4-point score: “complete disagreement” to “complete agreement” and forward scoring and calculate the mean. |

Extracurricular learning | From the student questionnaire b19: to investigate the effects of different types of extracurricular tutoring on students’ cognitive achievement, make the following code: “do not attend” is defined as 0; one or more participants in Mathematical Olympiad and general mathematics are classified as logic and coded as 1; one or more participants in Chinese composition and English are classified as language, and the code is 2; one or more participants in painting, calligraphy, musical instruments, dance, chess, and sports are classified as art, which is coded as 3; and the rest are treated as missing values. |

Extracurricular reading | From the student questionnaire b12: do you have many books at home (excluding textbooks and magazines) as a reference. From few to many, take a 5-point score, forward scoring, and calculate the mean. |

School level | |

Teachers’ gender | From the teacher (classroom teacher, Chinese, Mathematics, and English) questionnaire hrc01, chnb01, matb01, and engb01: 0 = male, 1 = female |

Teachers’ educational background | From the teacher (the classroom teacher, Chinese, Mathematics, and English teacher) questionnaire hrc04, chnb04, matb04, and engb04: 1 = education level of or under junior high school graduation, 2 = vocational high school/secondary specialized school/technical school graduation, 3 = high school graduation, 4 = college degree, 5 = undergraduate education (formal higher education), 7 = common senior high school, 6 = college diploma, 7 = graduate and above status.In the econometric model, take “under undergraduate status” defined as 0 and “undergraduate and above status” as 1. |

Teachers’ major | From the teacher (the classroom teacher, Chinese teacher, Mathematics teacher, and English teacher) questionnaire hrc05, chnb05, matb05, and engb05: 0 = yes, 1 = no. |

Teachers’ teaching age | From the teacher(classroom teacher, Chinese teacher, Mathematics teacher, and English teacher) questionnaire hrc07, chnb07, matb07, and engb07: 0 = not more than 10 years, 1 = 10 years and above |

Formal teacher or not | From the teacher questionnaire hrc11, chnb11, matb11, and engb11: 0 = formal teacher, 1 = informal teacher |

Whether teach concurrently | From the teacher questionnaire hra06, chnb06, and enga06: 0 = no, 1 = yes |

Teachers’ title | From the teacher questionnaire hrc12, chnb12, matb12, and engb12: 0 = no title, 1 = three-level title, 2 = second level title, 3 = first level title, 4 = senior title, 5 = high professional title. In the econometric model, 0 = non-senior title, 1 = senior title |

Books per student | From the school questionnaire, pla17, plb0101b, plb0102b, and plb0103b are calculated by the number of books and students in the school. |

Teaching equipment | From the school questionnaire pla15: whether the school is equipped with Class Access to ICTs to measure. |

Class sizes | From school questionnaire pla14: measured by the average number of seats in each classroom. |

Fixed assets | From the school questionnaire pla1201, pla1202, pla1204, pla1205, pla1206: 3-point score, 1 = no have, 2 = have, but the equipment needs to be improved, 3 = have, and equipment is well, and fixed assets are synthesized after obtaining the mean value. |

Teacher–student ratio | From the school questionnaire plc0107 |

Fixed Effect | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | Whole Model |
---|---|---|---|---|---|---|---|

Student level | |||||||

Parent’s educational background | 0.0147 *** (0.002) | 0.0140 *** (0.002) | 0.0125 *** (0.002) | 0.0147 *** (0.002) | 0.0144 *** (0.002) | 0.0144 *** (0.002) | 0.0114 *** (0.002) |

Family economic status | 0.0353 *** (0.009) | 0.0357 *** (0.009) | 0.0316 *** (0.009) | 0.0353 *** (0.009) | 0.0346 *** (0.009) | 0.0350 *** (0.009) | 0.0313 *** (0.009) |

Parent’s educational expectation for their children | 0.0578 *** (0.003) | 0.0581 *** (0.003) | 0.0306 *** (0.003) | 0.0577 *** (0.003) | 0.0577 *** (0.003) | 0.0578 *** (0.003) | 0.0306 *** (0.003) |

Peer influence | 0.0354 *** (0.003) | 0.0369 *** (0.003) | 0.0223 *** (0.003) | 0.0353 *** (0.003) | 0.0352 *** (0.003) | 0.0352 *** (0.003) | 0.0237 *** (0.003) |

Student gender | 0.0375 (0.001) | 0.0520 (0.001) | |||||

Student nationality | 0.0345 (0.01) | 0.0294 (0.01) | |||||

Only child or not | 0.02301 (0.02) | 0.0182 (0.02) | |||||

Self-education expectation | 0.0413 *** (0.004) | 0.0421 *** (0.004) | |||||

Learning attitude | 0.0155 *** (0.002) | 0.0169 *** (0.002) | |||||

Logic cram school | 0.0142 *** (0.002) | 0.0148 *** (0.002) | |||||

language cram school | 0.0191 *** (0.001) | 0.0168 *** (0.001) | |||||

Art cram school | −0.0650 *** (0.007) | −0.0624 *** (0.007) | |||||

Extracurricular reading | 0.0428 *** (0.005) | 0.0423 *** (0.005) | |||||

Faculty–student ratio | −0.0004 *** (0.0002) | −0.0002 *** (0.0002) | |||||

Teaching two or more classes concurrently | −0.2227 *** (0.036) | −0.168 *** (0.036) | |||||

Proportion of teachers with senior title | 0.112 * (0.022) | 0.0888 * (0.022) | |||||

Proportion of teachers with a bachelor’s degree or above | 0.1300 ** (0.04) | 0.0886 ** (0.04) | |||||

Proportion of female teachers | 0.1211 *** (0.003) | 0.0843 *** (0.003) | |||||

Proportion of teachers with a normal profession | −0.0476 ** (0.03) | −0.0429 *** (0.03) | |||||

Proportion of teachers with more than 10 years of teaching experience | −0.0022 *** (0.001) | −0.0035 *** (0.03) | |||||

Proportion of formal teachers | −0.0709 *** (0.002) | −0.0353 *** (0.002) | |||||

Facility conditions variable | have | have | have | have | have | have | have |

Random effect | |||||||

Level 1 variance | 0.7013491 | 0.7013491 | 0.6909673 | 0.6915774 | 0.6915636 | 0.6915629 | 0.6904896 |

Level 2 variance | 0.3799335 | 0.3675335 | 0.3376422 | 0.326925 | 0.3504121 | 0.3162254 | 0.260596 |

ICC | 0.351373 | 0.343848 | 0.328251 | 0.320986 | 0.336296 | 0.313782 | 0.273998 |

Fixed effect | Model 7 | Model 8 | Model 9 | Model 10 | Model 11 |
---|---|---|---|---|---|

Student level | |||||

Parent’s educational background | 0.0114 *** (0.002) | 0.0114 *** (0.002) | 0.0113 *** (0.002) | 0.0114 *** (0.002) | 0.0114 *** (0.002) |

Family economic status | 0.0318 *** (0.009) | 0.0319 *** (0.009) | 0.03147 *** (0.009) | 0.0318 *** (0.009) | 0.0315 *** (0.009) |

Parent’s educational expectation for their children | 0.0307 *** (0.003) | 0.0307 *** (0.003) | 0.0307 *** (0.003) | 0.0307 *** (0.003) | 0.0307 *** (0.003) |

Peer influence | 0.0238 *** (0.002) | 0.0238 *** (0.002) | 0.0238 *** (0.002) | 0.0238 *** (0.002) | 0.0238 *** (0.002) |

Average copies of books per student | −0.00007 *** (0.00002) | ||||

Teaching equipment | 0.0475 *** (0.001) | ||||

Class size | −0.0009 *** (0.00002) | ||||

Real estate | 0.0176 *** (0.003) | ||||

Student and teacher variables | Have | Have | Have | Have | Have |

Random effect | |||||

Level 1 variance | 0.6905276 | 0.6905311 | 0.690515 | 0.6905287 | 0.6904821 |

Level 2 variance | 0.260931 | 0.2598987 | 0.2608355 | 0.2578693 | 0.260236 |

ICC | 0.274243 | 0.2734538 | 0.274174 | 0.271813 | 0.273726 |

**Table 5.**Shapley and Owen Value Method Results for Student and Teacher Factors versus Facility Conditions Contributions to Students’ Cognitive Scores.

Variables Name | Shapley Value R^{2} (%) | Owen (Group 1) R^{2} (%) | Owen (Group 2) R^{2} (%) | Owen (Group 3) R^{2} (%) |
---|---|---|---|---|

Student nationality | 1.81 | 92.31 | 32.72 | 92.31 |

Student gender | 0.12 | |||

Teach two or more Extracurricular reading | 6.86 | |||

Only child or not | 3.08 | |||

Self-education expectation | 15.88 | |||

Learning attitude | 1.29 | |||

Logic cram school | 1.74 | |||

Language cram school | 1.07 | 59.59 | ||

Art cram school | 0.87 | |||

Classes concurrently or not | 14.32 | |||

Faculty–student ratio | 5.74 | |||

Proportion of teachers with a bachelor’s degree or above | 4.7 | |||

Proportion of female teachers | 7.93 | |||

Proportion of teachers with a normal profession | 5.42 | |||

Proportion of teachers with more than 10 years | 7.21 | |||

Proportion of formal teachers | 6 | |||

Proportion of teachers with senior title | 8.27 | |||

Average copies of books per student | 1.17 | 7.69 | 7.69 | 4.75 |

Teaching equipment | 2.33 | |||

Class size | 1.25 | |||

Fixed assets | 2.94 | 2.94 |

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**MDPI and ACS Style**

Wang, X.; Wang, A.
A Two-Level Hierarchical Linear Model Analysis of the Effect of Teacher Factors, Student Factors, and Facility Conditions on Students’ Cognitive Scores in Rural China. *Sustainability* **2022**, *14*, 7738.
https://doi.org/10.3390/su14137738

**AMA Style**

Wang X, Wang A.
A Two-Level Hierarchical Linear Model Analysis of the Effect of Teacher Factors, Student Factors, and Facility Conditions on Students’ Cognitive Scores in Rural China. *Sustainability*. 2022; 14(13):7738.
https://doi.org/10.3390/su14137738

**Chicago/Turabian Style**

Wang, Xiaoyan, and Anquan Wang.
2022. "A Two-Level Hierarchical Linear Model Analysis of the Effect of Teacher Factors, Student Factors, and Facility Conditions on Students’ Cognitive Scores in Rural China" *Sustainability* 14, no. 13: 7738.
https://doi.org/10.3390/su14137738